Direct measurement of ship body distortion using a laser beam

ABSTRACT

A laser light beam is directed to a cruciform target containing a series array of photo detectors on each arm. The light beam is perpendicular to the cruciform and is orbited about the cruciform center. A differential pulse width modulated (DPWM) wave is generated by the signals emitted from the photo detectors each time they are illuminated by the light beam, as the output of the photo detectors are connected to bi-stable flip-flops which are triggered into positive and negative states and whose pulse width depends upon the time for the rotating laser beam to travel between two arms displaced from each other by a 180* of arc. Angular distortions in the X axis and the Y axis are separately measured by two pairs of arms, the arms of each pair being displaced 180* from each other. The width of the pulse is proportional to the angular distortion.

mam States Patent (Cook et al.

[4 1 Feb. 5, 1974 DIRECT MEASUREMENT OF SP BODY DISTORTION USING A LASERBEAM The United States of America as represented by the Secretary of theNavy, Washington, DC.

Filed: Apr. 7, 1971 Appl. No.: 131,969

US. Cl. 356/152, 250/203 R Int. Cl. GOlb 11/26 Field of Search. 356/152;250/203 R; 244/3.l6

[56] References Cited UNITED STATES PATENTS FOREIGN PATENTS ORAPPLICATIONS 1,259,952 3/1961 France 250/203 R Primary ExaminerMaynardR. Wilbur Assistant ExaminerBuczinski, S. C. Attorney, Agent, or Firm-R.S. Sciascia; Q. E. Hodges A laser light beam is directed to a cruciformtarget containing a series array of photo detectors on each arm. Thelight beam is perpendicular to the cruciform and is orbited about thecruciform center. A differential pulse width modulated (DPWM) wave isgenerated by the signals emitted from the photo detectors each time theyare illuminated by the light beam, as the output of the photo detectorsare connected to bistable flip-flops which are triggered into positiveand negative states and whose pulse width depends upon the time for therotating laser beam to travel between two arms displaced from each otherby a 180 of arc. Angular distortions in the X axis and the Y axis areseparately measured by two pairs of arms, the arms of each pair beingdisplaced 180 from each other. The width of thepulse is proportional tothe angular distortion.

4 Claims, 9 Drawing Figures eooooo ooooooo PATENIEU 5'974 39 TUBZYE sum20F 45 William. "m" 'lmw' Fi 5a INVENTOR GEORGE W. COOK DAVID T. IVIILNEPATENIEB 51974 v sum 3 0? a ll 57' 47; Q50 lg IKE 49 49 I2 O'CLOCK 9O'CLOCK 6 dCLOCK 49 IM;

3 ocLocK GEORGE W. COOK DAVID T. IVIILNE I N VENTOR EXQOBZFE PNENTED FEB5 i974 QwQEA mQZmEmEmm ZCQQ INVENTOR AGENT ATTORNEY DIRECT MEASUREMENTOF SHIT BODY DISTORTION USTNG A LASER BEAM The invention describedherein may be manufactured and used by or for the Government of theUnited States of America for Governmental purposes without the paymentof any royalties thereon or therefor.

BACKGROUND OF THE INVENTION The prior art contains many devices used fordetecting angular variation about a reference axis and utilizing laserbeams. However, these prior art devices use a technique requiring thelaser beam be centered at a particular point and deviations from thatpoint are detected. These devices also use photo detectors which measurethe quantity and quality of the light beam. The resolution of theseprior art devices and their accuracy depend upon the resolution of thelaser beam and the quality of light that can be transmitted over afinite distance. In addition, these systems require complicated andcomplex signal processing circuitry for tracking the beams illuminationpoint and determining its displacement from the axial reference.

SUMMARY OF THE INVENTION A laser is mounted at one end ofa structure,the stern of a ship for example. A target to be illuminated by the laserbeam is mounted at another point in the structure spaced from the laserso that a reference axis is defined between the laser and the target bythe laser beam. Angular distortions of the body are then measuredrelative to the reference axis.

The target according to a first embodiment is a cruciform shape and hasa series of photo detectors arrayed on each arm. The plane of thecruciform is perpendicular to the direction of the laser light path. Thelaser beam is orbitly rotated about the center of the cruciform targetwith the result that it illuminates a photo detector in each arm as itsorbit path crosses that arm. The array of photo detectors in each of thefour arms are connected in parallel so that any one photo detectortriggered by the light beam energizes a bus line connected to theilluminated arm.

Each pair of arms displaced 180 from each other and arranged in a lineare connected to a bi-stable flipflop. As the rotating laser beamilluminates a first arm of the pair, the flip-flop is triggered into apositive state. When the laser beam traverses 180 of arc and illuminatesthe second arm of the pair, a second signal is received by the bi-stableflip-flop and its state changes. The pulse width of the positive state(i.e., the time for the rotating laser to traverse 180 of are changingthe fiip'flop from its positive to negative state) corresponds to theaxial displacement of the target from the light path. This result isapparent when one examines the effect of axial distortions on theposition of the cruciform center relative to the orbiting beam of light.

When no distortion is present. the path described by the beam of lightis a circle, illuminating photo detectors on each of the four arms, thedetectors located at equal distances from the center, and with thecircular path described having as its center, the center of thecruciform. Now, assuming that the structure undergoes a distortion aboutthe reference axis described by the light path, and the distortion beingin a vertical direction, the orbital light path center is then displacedfrom the center of the cruciform and relocated on one of the verticalarms. The time for the light beam to travel from a first horizontal armto a second arm 180 from the first arm will now be different than thetime it took the light beam to travel from a first horizontal arm to thesecond arm displaced 180 from the first arm, when no distortion waspresent and the circular light path was centered on the cruciformcenter.

A second embodiment of this invention has substituted for the cruciformtarget a rotating mirror with series arrays or banks of photo detectorsarranged parallel to the light path and at the 12 oclock, 3 oclock, 6oclock and 9 oclock positions. The rotating mirror has a 45 anglereflective surface and when no distortions are present the structure,the light path is reflected from the center of the prism and in acircular orbited path. The time interval for the orbited light beam totraverse two banks from each other is then the same.

When distortion is introduced in the body, the light beam is displacedfrom the center of the rotating mirror but is still deflected toward thearray of photo detectors. However, the effect as described above, withreference to the cruciform target, is repeated in this secondembodiment. The time interval between illumination of each of the banksin a pair arrayed 180 from each other is changed and this change isreflected in the pulse widths of the positive and negative output statesof each bi-stable flip-flop.

The pulse data is processed to produce a read out of the magnitude andrate of the angular variations over a period of time.

Accordingly, it is a first object of this invention to measure theangular distortion of a body about a reference axis.

It is a second object of the instant invention to use a rotating laserbeam to measure the time changes in target illumination and to generatesignals corresponding to these time changes.

It is a third object of this invention to use a rotating mirror,illuminated by the laser beam to generate signals corresponding to theangular displacement of the laser beam from the center of the rotatingmirror.

It is a fourth object of this invention to produce independent signaloutputs corresponding to body distortions in the X and Y directions.

These and other objects of the invention will become apparent as thefollowing description is read.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a side view ofa ship inwhich the laser beam distortion detector is mounted at the fore and aftends and this view is solely provided to orient the reader with regardto the system.

FIG. 2a shows the target of the first embodiment of this invention withthe orbital light path from the laser, with no distortion, superposedwith the light path from the laser when distortion is present.

FIG. 2b shows the target of FIG. 2a, with the orbital laser light pathand with no distortion superposed with the laser light path whendistortion is present and where the distortion is in the oppositedirection of the distortion as shown in FIG. 2a.

FIG. 3a shows the target of the second embodiment of this invention, asincluding a rotating 45 prism to deflect the incoming light beam tophoto detector banks arrayed at the 12 oclock, 3 oclock, 6 oclock and 9oclock positions, relative to the axis of rotation of the prism.

FIG. 3b shows individual views of the prism of FIG. 3a, at the 12, 3, 6and 9 o'clock positions and the resultant light paths when no distortionis present in the body and when distortion is present in the vertical Ydirection.

FIG. 4a, line A, shows the pulse wave train produced by the target of2a, when no distortion is present. FIG. 4a, lines B and C, show thepulse wave trains produced when distortion is present in a firstdirection (shown in FIG. 2a) relative to the reference axis.

FIG. 4b, line A, shows the pulse wave trains produced in the target ofFIG. 2b, when no distortion is present. FIG. 4b, lines B and C show thepulse wave trains produced when distortion is present in a seconddirection (shown in FIG. 2b) relative to the reference axis.

FIG. shows a system for processing the pulses of FIGS. 4a and 412.

DESCRIPTION OF THE PREFERRED EMBODIMENT Referring now to FIG. 1, a ship10 is shown with a laser light source 11 at one end and a target 13, asshown in FIGS. or 3a. The beam of light 15, defines a reference axis andis aligned with the target center when the ship body is at rest. Anystructural deformation about the axis defined by light path 15, willresult in the light from laser 11 shifting relative to the target andilluminating a different portion of the target.

Referring now to FIGS. 2a and 2b, the effect of the distortion on thetarget illumination by the light is seen. The target as shown in FIGS.20 and 2b is a cruciform having an arm 17 at the 12 o'clock position, anarm 19 at the 3 oclock position, an arm 21 at the 6 oclock position, andan arm 23 at the 9 oclock position. It is to be understood however, thatthe specific shape of the target may be different from the cruciformshown and may take other shapes in accordance with the principles ofthis invention. The plane of the cruciform is perpendicular to the pathof light 15, shown in FIG. 1. Arms 23 and 19, displaced 180 are a firstpair of detecting angular distortions in the Y direction. Arms 17 and21, arranged 180 from each other are a second pair used to detectangular distortions in the X direction. On each of the arms are a seriesof photo detectors, the numeral 22 indicating a typical detector on eacharm. In this embodiment '7 are shown, it being realized of course, thatthe size of the target and the number of photo detectors can be variedas circumstances dictate.

When the body is at rest, the laser orbital light path rotates clockwiseabout the center 25, of the target describing circular orbital path 24.The orbital path is of a constant frequency. When no distortion ispresent in the ship, the time interval between the illumination of arm23 and arm 19 is equal to the time interval between the illumination ofarm 19 and arm 23. And when the orbital light is centered on thecruciform center 25, the time interval between illumination of arm 17and arm 21 is equal to the interval between the successive illuminationof arm 21 and arm 17.

The laser beam 15, by illuminating arm 17, for example, causes a signalto be generated at one of the photo detectors (indicated by numeral 22)arranged on the arm. Photo detectors on each one of the arms 17, 19, 21and 23, are connected in parallel to a bus so that the light beamilluminating any photo detector on arm 17 for example, would generate asignal on the bus connected to arm 17. Arms 17 and 21 are designated apair as are arms 23 and 19. The bus from the parallel connected photodetectors of arm 17 are wired to a bistable flip-flop along with the busfrom the parallel connected photo detector from arm 21. The flip-flopresponsive to the illumination of the arm and the photo detectorstherein, changes state and holds this state until it receives a secondsignal when the light beam illuminates arm 21 and one of the photodetectors thereon. As the orbiting light path continues around from arm21, back to arm 17, the second state of the flip-flop is held untilanother signal is delivered to it by a photo detector on arm 17.

Similarly, the bank of photo detectors on arm 23 are wired in paralleland connected to a bi-stable flip-flop together with the bus from theparallel connected photo detectors on arm 19. The orbiting light pathilluminating arm 23, produces a signal in a photo detector thereon andchanges the state of the flip-flop. This state is held until theorbiting light path illuminates arm 19, producing a signal in one of thephoto detectors thereon and delivering a second signal to the flip-flop,changing its state. This second state is held until the orbiting lightpath once again illuminates arm 23, and one of the photo detectorsthereon once again changes its state. The changing states of theflip-flops are shown in the time diagrams of FIGS. 40 and 4b.

When no distortion relative to the reference axis defined by light beam15 is present in the body, the time duration for the orbiting beam totravel between each arm of a pair of arms arranged apart will be thesame. (As can be seen by inspection of light path 24 in FIG. 2a.) Theflip-flop will then produce an unmodulated pulse train with equal andpositive and negative states as shown in line A of FIGS. 4a and 4b.

The effect of distortion is to displace the orbiting beam pattern fromthe target center producing a differential pulse width modulated wave(DPWM). The DPWM wave pulse period and the time center I or center ofenergy is undisturbed by pulse width modulation as the pulse is expandedor contracted about its center point of energy t.

When the body is distorted so the center of the orbital light path 24 isshifted with respect to the center 25, of the cruciform to point 27(FIG. 2a), the time for the laser beam to travel between arm 23 and arm19, will be longer than for the laser beam to travel from arm 19 back toarm 23. It is seen therefore, that if a bistable flip-flop is programmedto be triggered to a positive state when a photo detector on arm 19 isilluminated, then for each period of the laser beam orbit, the wavetrain generated will be the DPWM train as shown in FIG. 4a, line B. ThisDPWM wave train corresponds to distortion in the Y direction and willhave a wider positive pulse and a narrower negative pulse width,proportional to the displacement of the center 27, of the orbiting lightpath in the Y direction from the cruciform center 25.

Similarly, when the distortion in the body causes the laser beam orbit24 to shift to center 27, (FIG. 2a), the time interval for the lightpath to travel from arm 17 to arm 21 will be longer than the time forthe light path to travel from arm 21 back to arm 17, If a bi-stable flipflop is programmed to be triggered positive when the beam of lighttriggers arm 21, the resultant wave train from this flip-flop will havea wider positive pulse width and a narrower negative pulse width asshown in line C of FIG. Ala, compared to the pulse train shown in lineA. The pulse width shown in line C of FIG. 4a, is pro portional to thedisplacement of the orbital light path in the X direction from cruciformcenter 25, and is proportional to the angular distortion of thestructure relative to light path 15.

Referring now to FIG. 2b, the target of FIG. 2a is shown with the lightpath center 29, displaced in an opposite direction from the light pathcenter 27, shown in FIG. 20. As can readily be seen by an examination ofthe displaced light path upon the cruciform and the DPWM wave shown inline B of FIG. 4b, the negative pulse Width corresponding to thedisplacement of center 29, from center 25 in the Y direction will bewider than the negative pulse width shown in line A of FIG. 4b. The DPWMwave produced by an orbiting light path centered at 29, and shown inline C of FIG. 4b, will have wider negative pulse width of the wavetrain shown in line A and with its width corresponding to thedisplacement of the illumination pattern centered at 29, relative to thecruciform center 25 and in the X direction.

Referring now to FIG. 5a, a system is shown for extracting theinformation in the pulse wave train shown in FIGS. 5a and 4b. The outputof a flip-flop shown is inputted to a pulse shaper at DPWM data input31. This input signal is shown in line A of FIG. 5b and represents theoutput of a flip-flop. At the same time a digital reference signalconsisiting of periodic impulses of a substantially higher frequencythan that DPWM wave is inputted to digital reference input 33. Theoutput of each of the pulse shapers is fed into an and gate 35, whichproduces an impulse output corresponding to the coincidence of thedigital reference with the positive excursions of the DPWM datum wave.As shown in line C of FIG. 5b, the pulses gated by and gate 35, and bythe differential pulse width modulated wave can then be fitted to anelectronic counter which can interpret the number of pulses received.

When this data processing technique is used, the digital referenceimpulses can be generated by the same device used to produce the orbitallight path and can provide a time reference wherein a constant number ofimpulses are generated for each period of the DPWM wave, correspondingto an orbit period.

The differential pulse width modulated wave may also be processedthrough a five pole Butterworth low pass filter to produce an analoguesignal. The filter should have a half power frequency set toapproximately 0.2 of the carrier frequency. A 50 db attenuation at thecarrier frequency is then attained which results in a 1 percentamplitude fidelity from zero frequency to 0.1 times the carrierfrequency. The reproduced analyzed data may be used to drive a combarray of bandpath filters for sophisticated spectral analysis or anytype of analogue data analysis desired.

Referring now to FIGS. 3a and 3b, a second embodiment according to theprinciples of this invention is shown. The stationary cruciform targetshown in FIGS. 2a and 2b, is replaced with a rotating prism 41, having a45 face angle. The prism is attached to shaft 43 and driven by a motivemeans about the axis of the shaft. Arrayed around the rotating prism atthe 12, 3, 6 and 9 oclock positions are banks of photo detectors inseries array parallel to the laser light beam 15. Each bank is wired toa bi-stable flip-flop as are the arms of the target shown in FIG. 2a.

As shown in FIG. 3a, photo detector bank 415 is at the 12 oclockposition, photo detector bank 47 is at the 9 oclock position and photodetector bank 49 is at a 6 o'clock position, the photo detector 50 atthe 3 oclock position is not shown in this view but it is to beunderstood that a fourth photo detector 50, at the 3 ocloclt positionwould be necessary in this embodiment.

The laser light beam is directed at point 57, on the face of the prism411i, and is deflected into a circular orbit by means of rotating mirror41, rotating about shaft 43. As the mirror rotates in a clockwisedirection, the orbiting light path sequentially illuminates each of thephoto detector arrays or banks.

When distortion is introduced into the body, the mirror 411 is displacedrelative to the light beam so the light beam impinges upon a differentpoint on the face of the prism 41.

The operation of the rotating target embodiment is explained by way ofexample, and by means of FIG. 3b, in conjunction with FIG. 3a. When theprism 41 is shifted by distortion in the body about the beam 15, thelight beam 15 is shifted away from point 57, on the face of prism 41 topoint 59. The light paths from the prism to banks 47 and 50, are asshown in the upper left hand and lower right hand positions of themirror 41 shown in FIG. 3b. When the prism 41 is rotated to the 9 oclockposition (FIG. 3b) the beam of light from point 59 has already passed bybank 47, setting the state of the flip-flop. When the mirror rotates tothe 3 oclock position, as shown in the lower right hand corner of FIG.3b, the beam of light from point 59 has not yet illuminated the photodetector in bank 50. It can be seen, therefore, that displacements of abody in the Y direction causing the light beam to shift from point 57 topoint 59, differentially modulates the pulse shown in line A of FIG. 4a,producing the pulse train of FIG. 4a line B. The wider positive outputpulse is produced when the mirror is rotated between the 9 oclock and 3oclock position and the narrower negative output pulse is produced whenthe mirror is rotated between the 3 oclock position and the 9 oclockposition. The result of this distortion, explained above, will result ina wave train as shown in line Bof FIG. la, assuming that the flip-flopis programmed to be triggered into its positive state when a photodetector at array 47 is illuminated.

On the other hand, if the body underwent distortion in the verticaldirection but in the opposite direction, the light beam would shift frompoint 57 to point 61. When the mirror ll is at the 9 oclock position,the light beam has not yet reached the photo detector in array 47. whenthe mirror has rotated to the 3 oclock position the light beam hasalready passed through and illuminated a photo detector in bank 50 andtriggered the flip-flop to the other state. It can be seen, therefore,that when distortion on a body causes the light beam to shift from point57 to 61, the pulse train of line A, FIG. 4b, is differentiallymodulated generating a DPWM wave as shown in line B of FIG. 4b.

The width of the DPWM wave of lines B, FIGS. 4a and 3b, would beproportional to the distortion of the body in the Y direction, about thereference axis. Similarly, the DPWM wave of line C of FIGS. 4a and 43b,would be proportional to the distortion of the body in the X directionabout the reference axis and would be produced by the sequential signalsproduced in banks 45 and 49.

The embodiment shown in H6. 3, is only described as to its operationwith regard to distortion in the Y direction, it is to be understoodthat any distortions in the X direction will produce the same resultsrotated 90.

The data processing system shown in FIGS. 5a and 5b, or the low passfilter system can be used to process the information produced by theembodiment shown in FIGS. 3a and 3b, the output wave train being thesame for the fixed target wave trains.

When the fixed target rotating beam system is utilized any suitablemethod for beam spinning may be used. One suitable method utilizes two45 angle prisms mounted on a circular plate with a first mirror mountedat the center of the plate to intercept the light beam and deflect it 90to a second 45 mirror mounted at the periphery of the plate. The seconddegree mirror then deflects the light beam outwardly to the target andthe plate is rotated so that the light beam from the second mirrordescribes an orbital path about an axis described by the beam emittedfrom the laser.

The mirrors on the beam spinner are adjusted so the radius of theprojected circle is twice the maximum expected X and Y displacement tobe measured. The reason is that the output of the system is proportionalto R sin 0. For the system to be susbstantially linear must be limitedto 30 and the sin 6 must then be less or equal to one-half.

Obviously many modifications and variations of the present invention arepossible in the light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims the inventionmay be practiced otherwise than as specifically described.

What is claimed is:

l. A system for measuring distortion of a body com prising:

a source of radiant energy mounted on the body for establishing ameasuring reference beam of coherent light;

a target for receiving and detecting said radiation fixedly mounted onthe body in linear spaced relationship to said source including aplurality of photo detector banks each equally radially spaced aroundthe reference axis of said beam and aligned therewith, thus defining atarget center;

a differential pulse width modulated wave generator electricallyconnected to said photo detector banks of said target producing pulsesof equal width when said body is undistorted and therefore said sourceand said target are aligned on the reference axis, and producing pulsesof unequal width when said body is distorted, the relative width of saidpulses being indicative of the degree of distortion; and

a reflective surface mounted at a 45 angle on a shaft rotatable coaxialwith the reference axis of said beam and being at the target center todeflect and orbit said beam radially onto said photo detector bankssurrounding the target center.

2.. The system of claim 1 wherein:

said banks include at least four, each positioned at the 12 oclock, 3oclock, and 9 oclock positions relative to the reference axis of saidbeam;

each of said banks spaced apart, being designated a pair;

a bistable flip-flop electrically connected to each pair and changingstate in response to a signal from each of said banks of said pair;

whereby the output of said flip-flop is a pulse wave of equal pulsewidths when said target is aligned with said reference axis.

3. The system of claim 2, wherein:

the time interval for said orbiting light beam to illuminate successivesemi-circular arcs of 180 are unequal when said body is distortedrelative to said reference axis, said flip-flop responsive to the saidsignal producing a differential pulse width modulated wave indicativedegree said distortion.

4. A method of measuring distortion of a body comprising the steps of:

projecting a beam of coherent radiant energy to illuminate and to definea reference axis to a target;

arranging detectors, responsive to said radiant energy, spaced about thecenter of said target;

driving the radiant energy in an orbital path about the center of saidtarget when no distortion is present;

distorting said projected beam from said orbital path about the centerof said target in response to distortion of the body;

producing a differential pulse width modulated signal proportionallyresponsive to the degree of distortion from said target detectors;

detecting the differential pulse width modulated signals; and

comparing the pulse widths of the differential pulse width modulatedwave when distortion is present to the pulse width when no distortion ispresent, to

measure the degree of distortion.

=l l =l l

1. A system for measuring distortion of a body comprising: a source ofradiant energy mounted on the body for establishing a measuringreference beam of coherent light; a target for receiving and detectingsaid radiation fixedly mounted on the body in linear spaced relationshipto said source including a plurality of photo detector banks eachequally radially spaced around the reference axis of said beam andaligned therewith, thus defining a target center; a differential pulsewidth modulated wave generator electrically connected to said photodetector banks of said target producing pulses of equal width when saidbody is undistorted and therefore said source and said target arealigned on the reference axis, and producing pulses of unequal widthwhen said body is distorted, the relative width of said pulses beingindicative of the degree of distortion; and a reflective surface mountedat a 45* angle on a shaft rotatable coaxial with the reference axis ofsaid beam and being at the target center to deflect and orbit said beamradially onto said photo detector banks surrounding the target center.2. The system of claim 1 wherein: said banks include at least four, eachpositioned at the 12 o''clock, 3 o''clock, and 9 o''clock positionsrelative to the reference axis of said beam; each of said banks spaced180* apart, being designated a pair; a bistable flip-flop electricallyconnected to each pair and changing state in response to a signal fromeach of said banks of said pair; whereby the output of said flip-flop isa pulse wave of equal pulse widths when said target is aligned with saidreference axis.
 3. The system of claim 2, wherein: the time interval forsaid orbiting light beam to illuminate successive semi-circular arcs of180* are unequal when said body is distorted relative to said referenceaxis, said flip-flop responsive to the said signal producing adifferential pulse width modulated wave indicative degree saiddistortion.
 4. A method of measuring distortion of a body comprising thesteps of: projecting a beam of coherent radiant energy to illuminate andto define a reference axis to a target; arranging detectors, responsiveto said radiant energy, spaced about the center of said target; drivingthe radiant energy in an orbital path about the center of said targetwhen no distortion is present; distorting said projected beam from saidorbital path about the center of said target in response to distortionof the body; producing a differential pulse width modulated signalproportionally responsive to the degree of distortion from said targetdetectors; detecting the differential pulse width modulated signals; andcomparing the pulse widths of the differential pulse width modulatedwave when distortion is present to the pulse width when no distortion ispresent, to measure the degree of distortion.